Help with jewel rarity

I have looked everywhere and cant seem to find the answer I'm looking for. I want to know what determines the rarity of each feystone. I read that there are 4 levels of fey stone, each with a different set of decorations. What I want to know is how can I get specific feystones, like, how can i get level 2 feystones instead of level 1. Is it the tempered investigations I have to do? Does the threat level determine which level feystone I get?